Whether or not you can keep it under $5000 depends in large part what you're counting in that total.
-$4000 to Disney
-$100+ license
-$175+ officiant
-$300+ hotel room (if you do a value resort for the four nights)
Total: $4575. These are pretty non-negotiable.
One way to keep food costs down might be to try a buffet (Ohana seems popular). If you can keep it to $30 per person, then with twenty people you could get away with about $600 (obviously alcohol/tax could make that go up, guest count could make it go down).
Then, there's makeup and formal wear, plus any extras like additional flowers, additional photography/videography, and things like favours/cake upgrades/champagne/guest book/unity candle, etc.
As you can see, whether or not you're able to do $5000 really does depend on what you're counting.
Good luck!